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# Isotopic age dating patterson

We will skip the isochron derivation, but you can find it elsewhere[1].

Imagine going way back in time and looking at some lava that is cooling to become a rock.

It naturally has different concentrations of Rb and Sr in different parts of the rock because these don’t necessarily mix perfectly. Once it cools all the way and crystallizes, it is considered "born" and atoms can no longer come in or out of the system.

Uranium and lead concentration data indicate that the isotopic lead ages for the Bruderheim chondrite are concordant within approximately 20%.

This contrasts with lead data in the literature for chondrites, which consistently indicate discordant isotopic lead ages due to large excesses of radiogenic lead by factors of two or more.

The slope of the line can then be solved for $$t$$, giving us the age of the rock.

As a bonus, the intercept ($$b$$) of the line tells us the value of $$\text_$$ because we know the line was flat when the age of the rock was zero. Note that the values of the axes are actually normalized by Sr86 because the mass spectrometers used to take these measurements are much more accurate at relative values than they are at absolutes.At this point, its radiometric clock starts ticking.Though the Rb and Sr concentrations differ, it’s safe to assume that the isotopic makeup of Sr and of Rb is the same everywhere.Unfortunately, the geochron equation above is transcendental, meaning there’s no algebraic solution for it and it has to be solved numerically.Conveniently, this is very trivial with a few lines of Python.This was calculated by taking precise measurements of things in the dirt and in meteorites and using the principles of radioactive decay to determine an age. The rest will have decayed into a different nuclide (called a nuclide).Several radioactive nuclides exist in nature with half-lives long enough to be useful for geologic dating.So to figure out the age of the Earth, we have to look somewhere else... Earth has a molten magma layer and plate tectonics, so the "closed system" requirement of these radiometric dating methods is sometimes difficult to satisfy for Earth itself.Meteorites, on the other hand, have been floating around in space since the solar system was formed.The isotopic lead ages for Pultusk may be concordant; those for a sample of Richardton are not.The lack of concordance for Richardton is not due to the analytical procedures, rather it is likely a result of the handling history of the chondrite prior to analysis.